You could upload your SRA files to Galaxy and use the SRA to FASTQ converter, however I'd strongly recommend you try to get the SRA toolkit working on your Windows machine.
There is now a new release of the SRAtoolkit (2.9.1) that introduces fasterq-dump, a multithreaded follow-up of
fastq-dump. Had a quick look at it and the increase in speed is notable, but (and I really do not understand this in 2018 at all) there is no longer a --gzip option, requiring additional post-processing. I really do not understand why, in times where projects may require the processing of terabytes of .sra data, a tool can lack a compression option, flooding the hard drives with Tb of unnecessarily large amounts of data (the last sentence is of course thinking aloud). I will probably stick with parallel-fastq-dump, given that files (e.g. from dbGaP) are not backed up on ENA.
Not quite an answer to the question you are asking, but the ENA (European Nucleotide Archive) has all publically available SRA samples for download directly as fastq. The download will take much longer (unless you use aspera), but the you more than make up for it in conversion time.